Screening of Possibly Incompetent Agents and Welfare Analysis without Common Priors

Accepting a contract with a high performance sensitivity is normally interpreted as a signal of high ability. However, an extremely high self-assessment may be an incompetent forecast by an incompetent worker. The authors do not want a portfolio manager who expects nearly riskfree returns of 50%/year! We study a model in which optimistic forecasters have low ability. In one type of equilibrium, a low performance sensitivity screens out the incompetent agents. In another, not applicable for financial markets, agents are wealthy enough for the principal to select the incompetent agent who covers the downside (as in a vanity press). Doing welfare analysis of this phenomenon is challenging because agents have different priors and it is not clear what beliefs to use in evaluating welfare. Computing utility using agents’ subjective beliefs, the outcome is relatively efficient because arbitraging the difference in beliefs improves welfare. However, in the objectivist view that there are true underlying probabilities, arbitraging beliefs adds noise and is inefficient. In either case, equilibrium tends to be second-best efficient since the agents’ selfselection constraints, which use their own beliefs, undermine an objectivist social planner’s efforts. Agents disagree with the social planner and are unwilling to move to the allocation in which the planner thinks they are better off. JEL Codes: G34 M51 M52 ∗Corresponding author. University of Texas at Dallas, P.O. BOX 830688 SM31, Richardson, TX 75083-0688. E-mail: [email protected]. †Washington University in St. Louis.